Curved-surface generating method and program, and three-dimensional shape processing apparatus

ABSTRACT

A plurality of representative points are selected from a group of points obtained as results of shape measurement of an object, respective principal curvatures are calculated at the representative points on the basis of positional relationships between the representative point and a plurality of points existing around the representative point, a line of curvature is created on the basis of the principal curvatures of the representative points and a curved surface is generated using this line of curvature.

TECHNICAL FIELD

The present invention relates to a curved-surface generating method forgenerating a curved surface from a group of points formed of a pluralityof measurement points obtained as the results of shape measurement of anobject.

BACKGROUND ART

Conventionally, when reproducing, in parameter space, athree-dimensional shape model for use in CAD (Computer Aided Design) orCAM (Computer Aided Manufacturing) from the results of shape measurementof an object, a known technique is to create polygonal surfaces, such astriangles etc., by connecting each of a group of points with straightlines.

For example, Japanese Unexamined Patent Application, Publication No.2003-346182 discloses a three-dimensional polygon data creating methodwhich can obtain polygon data for an object surface with superiorperformance and stability from three-dimensional group-of-points datawhich are the results of shape measurement of an object, using amatching triangles method.

-   Patent Document 1:-   Japanese Unexamined Patent Application, Publication No. 2003-346182    (pages 2 to 8, and FIGS. 1 and 4).

DISCLOSURE OF INVENTION

However, in the invention of Patent Document 1 described above, becausethe shape is defined with polygonal approximations, there are someapproximation errors for undevelopable curved surfaces among curvedsurfaces. Conventionally, to reduce these approximation errors, atechnique for creating polygons as finely as possible to achieve preciseapproximation is used. However, with this technique, the amount of databecomes enormous, resulting in the problem that, in practice, the amountof required computer memory increases.

Furthermore, with the conventional technique, because surface normalsare determined from polygons, it is not possible to obtain accuratenormals according to the curvature of the curved surface. Therefore,there is a problem in that an error is included in the reproduced curvedsurface, and it is not possible to generate a curved surface with goodprecision.

The present invention has been conceived to solve the problems describedabove, and an object thereof is to provide a curved-surface generatingmethod and program and a three-dimensional shape processing apparatuswhich can reduce the amount of data and generate a curved surface withhigh precision.

In order to solve the problems described above, the present inventionemploys the following solutions.

A first aspect of the present invention is a curved-surface generatingmethod for generating a curved surface from a group of points formed ofa plurality of measurement points obtained as results of shapemeasurement of an object, the curved-surface generating method includinga representative-point selection step of selecting a plurality ofrepresentative points from the group of points; a principal-curvaturecalculating step of calculating respective principal curvatures at eachof the representative points on the basis of positional relationshipsbetween each representative point and a plurality of the measurementpoints existing around this representative point; a line-of-curvaturecreating step of creating a line of curvature on the basis of theprincipal curvatures at each representative point; and a curved-surfacegenerating step of generating a curved surface by using the line ofcurvature.

With this curved-surface generating method, after selecting theplurality of representative points from the group of points, theprincipal curvature at each representative point is calculated on thebasis of the positional relationships between each representative pointand the points existing around it, and the line of curvature is createdfrom these principal curvatures. Then, by using this line of curvature,the curved surface is reproduced with a curve-surface reproductiontechnique or the like. In this way, the plurality of points around eachrepresentative point are taken as auxiliary points for obtaining theprincipal curvatures. Therefore, the reproduced curved surface can berepresented using only the representative points. Accordingly, althoughthe curved surface can be reproduced with an extremely small group ofpoints, because the curved surface is reproduced using information aboutall points, it is possible to reproduce the curved surface with highprecision.

In the curved-surface generating method described above, theprincipal-curvature calculating step may include a step of setting anormal at each representative point; a step of generating elementvectors by joining each representative point and each points existingaround this representative point; and a step of determining theprincipal curvatures on the basis of relationships between the normaland the element vectors.

With this method, a normal is set at each representative point and thesame number of element vectors as the number of points existing aroundthe representative point are generated by joining each representativepoint and the points existing around this representative point.Therefore, it is possible to obtain the principal curvatures with asimple technique on the basis of the relationships between the normal ofthe representative point and each element vector generated around therepresentative point.

In the curved-surface generating method described above, theprincipal-curvature calculating step may include a step of setting anormal at each representative point; a tangential-vector setting step ofsetting a tangential vector that is orthogonal to the normal; a step ofgenerating element vectors by joining each representative point and eachpoint existing around this representative point; a step of calculatingangles formed by the tangential vector and the element vectors aroundthe normal; a step of calculating angles formed by a tangential planeincluding the tangential vector and planes including the element vectorsand defining the angles as curvatures; a step of creatingangle-curvature tables by plotting the calculation results on ahorizontal axis in angle-curvature tables; and a step of obtaining theprincipal curvatures on the basis of the curvature tables.

In this way, normal is set at the representative point and tangentialvector which is orthogonal to the normal is set. In addition, by joiningthe representative point and each point existing around therepresentative point, the same number of element vectors as the numberof points existing around the representative point is generated. Then,the angles that the tangential vector and the element vectors formaround the normal are calculated, the angles formed by the tangentialplane including the tangential vector and the planes including theelement vectors are calculated for each element vector, and thesecalculation results are plotted in angle-curvature tables in which angleis shown on the horizontal axis and curvature is shown on the verticalaxis to create angle-curvature tables. Thus, by obtaining the maximumcurvature and the minimum curvature in these angle-curvature tables, itis possible to easily obtain the principal curvatures.

In the curved-surface generating method described above, theprincipal-curvature calculating step may include a step of setting anormal at each representative point; a tangential-vector setting step ofsetting a tangential vector that is orthogonal to the normal; a step ofgenerating element vectors by joining each representative point and eachpoint existing around this representative point; a step of calculatingangles formed by the tangential vector and the element vectors aroundthe normal; a step of calculating angles formed by a tangential planeincluding the tangential vector and planes including the element vectorsand defining the angles as curvatures; a step of creatingangle-curvature tables by plotting the calculation results on ahorizontal axis in angle-curvature tables; an extraction step ofextracting only a fundamental frequency from the curvature tables; and aprincipal-curvature obtaining step of obtaining the principal curvaturesfrom the angle-curvature table on the basis of the fundamentalfrequency.

In this way, a normal is set at each representative point and atangential vector which is orthogonal to the normal is set. In addition,by joining each representative point and each point existing around thisrepresentative point, the same number of element vectors as the numberof points existing around the representative point is generated. Then,at each representative point, the angles formed by the tangential vectorand the element vectors around the normal are calculated, the anglesformed by the tangential plane including the tangential vector and theplanes including the element vectors are calculated for each elementvector, and these calculation results are plotted in angle-curvaturetables in which angle is shown on the horizontal axis and curvature isshown on the vertical axis to create angle-curvature table. Then, onlythe fundamental frequency is extracted from these angle-curvaturetables. Extraction of this fundamental frequency obtains the fundamentalfrequency by, for example, regarding the angle-curvature table as atime-series table and performing, for example, a fast Fourier transformon this table. Thereafter, by performing, for example, an inverse fastFourier transform on this fundamental frequency, it is possible toobtain an angle-curvature table in which only the fundamental frequencyis reflected. Because this angle-curvature table is a high-precisiontable from which noise is eliminated and accurate values are reflected,it is possible to obtain the principal curvatures with extremely highprecision.

In the curved-surface generating method described above, theprincipal-curvature calculating step may include a step of generatingelement vectors by joining each representative point and each pointexisting around this representative point; a step of determining a groupof normal vectors at each representative point by calculating vectorproducts of the element vectors; and a step of determining an averagevector of the group of normal vectors and defining the average vector asa normal vector at each of the representative points.

With this method, by obtaining the vector products of the plurality ofelement vectors generated by joining each representative point and eachof the points existing around this representative point, the group ofnormal vectors at each representative point is obtained, and the averagevector of this group of normal vectors is defined as the normal vectorof that representative point. Therefore, it is possible to set a normalvector with higher reliability by using information about a plurality ofpoints. Accordingly, it is possible to improve the precision of thecurved surface reproduction.

A second aspect of the present invention is curved-surface generatingprogram for executing, on a computer system, curved-surface generatingprocessing for generating a curved surface from a group of points formedof a plurality of measurement points obtained as results of shapemeasurement of an object, the curved-surface generating programincluding a representative-point selection step of selecting a pluralityof representative points from the group of points; a principal-curvaturecalculation step of calculating respective principal curvatures at eachrepresentative point on the basis of positional relationships betweeneach representative point a plurality of the measurement points existingaround this representative point; a line-of-curvature creating step ofcreating a line of curvature on the basis of the principal curvature ateach representative point; and a curved-surface generating step ofgenerating a curved surface by using the line of curvature.

A third aspect of the present invention is a three-dimensional shapeprocessing apparatus which is provided with a curved-surface generatingprogram and which generates a curved surface from a group of pointsformed of a plurality of measurement points obtained as results of shapemeasurement of an object by executing the curved-surface generatingprogram, wherein the curved-surface generating program includes arepresentative-point selection step of selecting a plurality ofrepresentative points from the group of points; a principal-curvaturecalculating step of calculating respective principal curvatures at eachrepresentative point on the basis of positional relationships betweeneach representative point and a plurality of the measurement pointsexisting around this representative point; a line-of-curvature creatingstep of creating a line of curvature on the basis of the principalcurvature at each representative point; and a curved-surface generatingstep of generating a curved surface by using the line of curvature.

The present invention affords an advantage in that it is possible togenerate a curved surface with high precision, while reducing the amountof data.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing, in outline, the configuration of athree-dimensional shape processing apparatus according to a firstembodiment of the present invention.

FIG. 2 is a flowchart showing the procedure of a curved-surfacegenerating method according to the first embodiment of the presentinvention.

FIG. 3 is a diagram for explaining representative points.

FIG. 4 is a diagram for explaining a principal-curvature calculationstep.

FIG. 5 is a flowchart showing the procedure of the principal-curvaturecalculation step according to the first embodiment of the presentinvention.

FIG. 6 is a diagram for explaining the principal-curvature calculationstep.

FIG. 7 is a diagram showing an example of an angle-curvature tableaccording to the first embodiment of the present invention.

FIG. 8 is a diagram showing a fast Fourier transformed table accordingto a second embodiment of the present invention.

FIG. 9 is a diagram showing an example of an angle-curvature tableaccording to the second embodiment of the present invention, in whichonly a fundamental frequency is reflected.

FIG. 10 is a diagram showing an example of an angle-curvature tabledepicting a line of curvature obtained from measurement values and aline of curvature obtained on the basis of Euler's formula.

BEST MODE FOR CARRYING OUT THE INVENTION

An embodiment of a three-dimensional processing apparatus for realizinga curved-surface generating method according to the present inventionwill be described below with reference to the drawings.

First Embodiment

FIG. 1 is a block diagram showing, in outline, the configuration of athree-dimensional shape processing apparatus according to a firstembodiment of the present invention. As shown in FIG. 1, thethree-dimensional shape processing apparatus according to thisembodiment, which is a computer system such as a CAD (Computer AidedDesign) or CAM (Computer Aided Manufacturing) system, is formed of a CPU(central processing unit) 1, a main storage device 2 such as a RAM(Random Access Memory), a secondary storage device 3 such as an HDD(Hard Disk Drive), an input device 4 such as a keyboard or mouse, anoutput device such as a monitor or printer, and so forth.

Various programs are stored in the secondary storage device 3, and theCPU 1 realizes various types of processing by reading programs from thesecondary storage device 3 into the main storage device 2 such as theRAM and executing them.

Next, curved-surface generating processing (curved-surface generatingmethod) for generating a curved surface from a group of points, in thethree-dimensional shape processing apparatus having the above-describedconfiguration, will be described with reference to the drawings. Theprocessing shown below is realized by, for example, the CPU 1 reading acurved-surface generating program stored in the secondary storage device3 into the main storage device 2 such as the RAM and executing it.

First, the CPU 1 acquires group-of-points data from a plurality ofmeasurement points obtained as a result of shape measurement of anobject. This group-of-points data may be stored in advance in a memory,such as the secondary storage device 3, installed in thethree-dimensional shape processing apparatus, or it may be obtainedonline from another external device. In the present invention, the wayin which this group-of-points data is acquired is not particularlylimited.

When the group-of-points as described above (hereinafter referred to as“group of points”) is acquired, a plurality of representative points areselected from the group of points (step SA1 in FIG. 2: representativepoints selection step). For example, in a group of points such as thatshown in FIG. 3, a plurality of points are selected as representativepoints P0. Then, based on the positional relationship between eachrepresentative point P0 selected in step SA1 and a plurality of pointsexisting around this representative point P0, the respective principalcurvatures at each of the representative points P0 are calculated (stepAS2: principal-curvature calculation step).

Details of the principal-curvature calculation step are described belowby giving as an example a group of points belonging to an arbitrarilyselected area Q from among the group of points shown in FIG. 3.

First, as shown in FIG. 4, element vectors L01, L02, L03, and L04 aregenerated by joining the representative point P0 to the points P1, P2,P3, and P4, respectively, which exist around P0 (step SB1 in FIG. 5).

Then, calculating the vector products of all combinations of the elementvectors L01, L02, L03, and L04 yields a group of normal vectors (notshown in the drawing) at the representative point P0 (step SB2 in FIG.5). Then, an average vector of the group of normal vectors isdetermined, and this average vector is defined as a normal vector n atthe representative points P0 (step SB3 in FIG. 5).

Next, principal curvatures are determined on the basis of the respectiverelationships between this normal vector n and the element vectors L01,L02, L03, and L04. Specifically, a tangential vector t that isorthogonal to the normal n is set, the angles which this tangentialvector t and each of the element vectors L01, L02, L03, and L04 formaround the normal n are calculated, and the angles formed by atangential plane including the tangential vector and planes includingeach of the element vectors L01, L02, and L04 are calculated as thecurvatures (step SB4 in FIG. 5).

For example, when the element vector L02 shown in FIG. 4 has therelationship shown in FIG. 6 with respect to the representative pointP0, an angle θ2 formed by the tangential vector t and the vectorcomponent L02 (XY) in the tangential plane of the element vector L02 iscalculated, and the angle formed by the plane including the elementvector L02 and the tangential plane including the tangential vector t isobtained as a curvature K2.

In a similar fashion, angles θ and curvatures K are also calculated forpoint P1, P3, and P4 shown in FIG. 4.

Once such calculations for the points existing around the representativepoint P0 have been completed, angle-curvature tables are created byplotting the calculation results in angle-curvature tables showing angleθ on the horizontal axis and curvature K on the vertical axis andfitting these points using Euler's law (step SB5 in FIG. 5). As aresult, an angle-curvature table such as that shown in FIG. 7, forexample, is obtained. Points may be plotted in the angle-curvature tablein parallel with the calculation.

Then, a maximum curvature Kmax and a minimum curvature Kmin in thisangle-curvature table are obtained as the principal curvature (step SB6in FIG. 5).

Then, by performing the respective principal-curvature calculationprocesses described above for each of the representative points P0 setin the group of points shown in FIG. 3, the maximum curvature Kmax andthe minimum curvature Kmin at each of the representative points P0 areobtained.

When the principal curvatures at each of the representative points P0are obtained, a line of curvature is created by connecting theseprincipal curvatures (step SA3 in FIG. 2: line-of-curvature creationstep).

Then, a curved surface is generated by a curved-surface reproductiontechnique using this line of curvature (step SA4 in FIG. 2:curved-surface generating step). For example, Gaussian mapping/inversemapping are performed to generate a curved surface on the basis of theline of curvature. Specifically, the curved surface is generated byinterpolation of the curved surface after performing a coordinatetransformation to a parameter space in which Euclidean geometry isestablished.

As described above, with the curved-surface generating method accordingto this embodiment, after selecting a plurality of representative pointsP0 from the group of points, the principal curvatures are calculated atthe representative points P0 on the basis of the positionalrelationships between each representative point P0 and the pointsexisting around it, and a line of curvature is created from theseprincipal curvatures. Then, by using this line of curvature, a curvedsurface is generated by a curved-surface reproduction technique or thelike. In this way, a plurality of points around each representativepoint P0 are taken as auxiliary points for obtaining the principalcurvatures, and a curved surface is reproduced. Therefore, thereproduced curved surface can be represented using only therepresentative points P0. Accordingly, although the curved surface canbe represented with an extremely small group of points, because thecurved surface is generated using information about all points, it ispossible to generate the curved surface with high precision. As aresult, it is possible to reduce the amount of data, thus making itpossible to speed up the processing.

For example, if a group of points consisting of a plurality ofmeasurement points obtained as the results of shape measurement of anobject contains 3 million points, when using the curved-surfacegenerating method according to this embodiment, it is possible torepresent a curved surface by using several thousand points.

Second Embodiment

Next, a curved-surface generating method according to a secondembodiment of the present invention will be described with reference tothe drawings. The difference between the curved-surface generatingmethod according to this embodiment and the curved-surface generatingmethod according to the first embodiment is the addition of thefollowing step in the principal-curvature calculation step (step SA2 inFIG. 2) according to the first embodiment described above in order tofurther improve the precision of the curved-surface generation.

That is, in the curved-surface generating method of this embodiment, astep of extracting only a fundamental frequency from the angle-curvaturetable after creating the angle-curvature table (step SB5) and a step ofrecreating the angle-curvature table for this fundamental frequency areadded to the detailed procedure of the principal-curvature calculatingstep according to the first embodiment shown in FIG. 4, and theprincipal curvature is obtained from this recreated angle-curvaturetable.

The step of extracting only the fundamental frequency from theangle-curvature table can be realized by the following technique, forexample.

Frequency components (spectrum) are obtained by fast Fouriertransforming (FFT) the angle-curvature table, and in the fast Fouriertransformed table, the frequency at which the spectrum shows a maximumvalue is extracted as the fundamental frequency. An example of the fastFourier transformed table is shown in FIG. 8. In this fast Fouriertransformed table, the horizontal axis is frequency and the verticalaxis is the amplitude spectrum.

Then, by inverse fast Fourier transforming (IFFT) the fundamentalfrequency component extracted in this way, it is possible to obtain anangle-curvature table in which only the fundamental frequency componentis reflected. An example of an angle-frequency table in which only thefundamental frequency component is reflected is shown in FIG. 9. As isclear from this figure, noise is removed from the angle-curvature tableaccording to this embodiment, and it has higher precision compared tothe angle-curvature table according to the first embodiment shown inFIG. 7.

Then, by obtaining the maximum curvature Kmax and the minimum curvatureKmin from this angle-curvature table, it is possible to obtain theprincipal curvature with an extremely small error.

As described above, with the curved-surface generating method accordingto this embodiment, because the principal curvature is obtained from theangle-curvature table with extremely small error, it is possible togenerate a curved surface with extremely high precision. Accordingly, acurved surface generated from a group of points can be assumed to be asmooth surface.

In the embodiment described above, extraction of the fundamentalfrequency is achieved using a fast Fourier transform (FFT), but it isnot limited to this method. For example, it is also possible to use theMEM (Maximum Entropy Method), the BT method (Blackman-Tukey Method), awavelet method, and so on.

In the embodiment described above, in step SB3 in FIG. 5, the averagevector of the group of normal vectors is defined as the normal vector.As described below, however, this average vector may be furthercorrected and the corrected average vector may be defined as the normalvector.

First, in the embodiment described above, the tangential vector which isorthogonal to the average vector is set, and the angle-curvature tableas shown in FIG. 7 is created from the respective positionalrelationships between this tangential vector and each of the elementvectors L01, L02, L03, and L04. Here, when the average vector describedabove is not actually a tangential vector, the curve depicted in theangle-curvature table is not an exact cosine wave based on Euler'sformula, as shown by the dotted line is FIG. 10, nor a cosine wave butis a curve such as that shown by the solid line in FIG. 10, in otherwords, a curve whose phase is shifted from the curve based on Euler'sformula.

Thus, while finely swinging the average vector to an arbitrary angle toeliminate this error, more concretely, by changing the orientation ordirection angle of the average vector shown in FIG. 6 by a small amountat a time, the curve depicted in the angle-curvature table (the solidline in FIG. 10) is corrected, and the average vector when this curve issubstantially aligned with the curve based on Euler's formula (thedotted line in FIG. 10) is defined as the normal vector.

With this approach, because it is possible to determine the normalvector based on Euler's formula, it is possible to increase theprecision.

Although the embodiments of the present invention have been describedabove with reference to the drawings, the actual configuration is notlimited to these embodiments. Various modifications are possible so longas they do not depart from the spirit of the invention.

1. A curved surface generating method, performed by a computer aideddesign system or a computer aided manufacturing system including acomputer, for generating a curved surface from a group of points formedof a plurality of measurement points obtained as results of shapemeasurement of an object, comprising: a representative-point selectionstep, performed by said computer, of selecting a plurality ofrepresentative points from the group of points; a principal-curvaturecalculating step, performed by said computer, of calculating respectiveprincipal curvatures at each of the representative points on the basisof positional relationships between each representative point and aplurality of the measurement points existing around this representativepoint; a line-of-curvature creating step, performed by said computer, ofcreating a line of curvature on the basis of the principal curvatures ateach representative point; and a curved-surface generating step,performed by said computer, of generating a curved surface by using theline of curvature, wherein the principal-curvature calculating stepincludes, a step of setting a normal at each representative point; atangential-vector setting step of setting a tangential vector that isorthogonal to the normal; a step of generating element vectors byjoining each representative point and each point existing around thisrepresentative point; a step of calculating angles formed by thetangential vector and the element vectors around the normal; a step ofcalculating angles formed by a tangential plane including the tangentialvector and planes including the element vectors and defining the anglesas curvatures; a step of creating angle-curvature tables by plotting thecalculation results on a horizontal axis in angle-curvature tables; anda step of obtaining the principal curvatures on the basis of thecurvature tables.
 2. A curved-surface generating method according toclaim 1, wherein the principal-curvature calculating step includes astep of setting a normal at each representative point; a step ofgenerating element vectors by joining each representative point and eachpoints existing around this representative point; and a step ofdetermining the principal curvatures on the basis of relationshipsbetween the normal and the element vectors.
 3. A curved-surfacegenerating method according to claim 1, wherein the principal-curvaturecalculating step includes a step of setting a normal at eachrepresentative point; a tangential-vector setting step of setting atangential vector that is orthogonal to the normal; a step of generatingelement vectors by joining each representative point and each pointexisting around this representative point; a step of calculating anglesformed by the tangential vector and the element vectors around thenormal; a step of calculating angles formed by a tangential planeincluding the tangential vector and planes including the element vectorsand defining the angles as curvatures; a step of creatingangle-curvature tables by plotting the calculation results on ahorizontal axis in angle-curvature tables; an extraction step ofextracting only a fundamental frequency from the curvature tables; and aprincipal-curvature obtaining step of obtaining the principal curvaturesfrom the angle-curvature table on the basis of the fundamentalfrequency.
 4. A curved-surface generating method according to claim 1,wherein the principal-curvature calculating step includes a step ofgenerating element vectors by joining each representative point and eachpoint existing around this representative point; a step of determining agroup of normal vectors at each representative point by calculatingvector products of the element vectors; and a step of determining anaverage vector of the group of normal vectors and defining the averagevector as a normal vector at each of the representative points.
 5. Acomputer-readable storage medium storing a curved-surface generatingprogram for executing, on a computer system, curved-surface generatingprocessing for generating a curved surface from a group of points formedof a plurality of measurement points obtained as results of shapemeasurement of an object, the curved-surface generating programcomprising: a representative-point selection step of selecting aplurality of representative points from the group of points; aprincipal-curvature calculation step of calculating respective principalcurvatures at each representative point on the basis of positionalrelationships between each representative point a plurality of themeasurement points existing around this representative point; aline-of-curvature creating step of creating a line of curvature on thebasis of the principal curvature at each representative point; and acurved-surface generating step of generating a curved surface by usingthe line of curvature, wherein the principal-curvature calculating stepincludes, a step of setting a normal at each representative point; atangential-vector setting step of setting a tangential vector that isorthogonal to the normal; a step of generating element vectors byjoining each representative point and each point existing around thisrepresentative point; a step of calculating angles formed by thetangential vector and the element vectors around the normal; a step ofcalculating angles formed by a tangential plane including the tangentialvector and planes including the element vectors and defining the anglesas curvatures; a step of creating angle-curvature tables by plotting thecalculation results on a horizontal axis in angle-curvature tables; anda step of obtaining the principal curvatures on the basis of thecurvature tables.
 6. A three-dimensional shape processing apparatus,comprising: a computer-readable storage medium storing a curved-surfacegenerating program and which generates a curved surface from a group ofpoints formed of a plurality of measurement points obtained as resultsof shape measurement of an object by executing the curved-surfacegenerating program, wherein the curved-surface generating programincludes a representative-point selection step of selecting a pluralityof representative points from the group of points; a principal-curvaturecalculating step of calculating respective principal curvatures at eachrepresentative point on the basis of positional relationships betweeneach representative point and a plurality of the measurement pointsexisting around this representative point; a line-of-curvature creatingstep of creating a line of curvature on the basis of the principalcurvature at each representative point; and a curved-surface generatingstep of generating a curved surface by using the line of curvature,wherein the principal-curvature calculating step includes, a step ofsetting a normal at each representative point; a tangential-vectorsetting step of setting a tangential vector that is orthogonal to thenormal; a step of generating element vectors by joining eachrepresentative point and each point existing around this representativepoint; a step of calculating angles formed by the tangential vector andthe element vectors around the normal; a step of calculating anglesformed by a tangential plane including the tangential vector and planesincluding the element vectors and defining the angles as curvatures; astep of creating angle-curvature tables by plotting the calculationresults on a horizontal axis in angle-curvature tables; and a step ofobtaining the principal curvatures on the basis of the curvature tables.